A novel high-order low-dissipation TENO-THINC scheme for hyperbolic conservation laws

The high-order low-dissipation shock-capturing scheme is important for compressible fluid simulations, in particular for cases where both shock and turbulence present. However, the competing requirements for resolving the small-scale turbulence structures with low dissipation and capturing the discontinuities sharply render it nontrivial for numerical development. In this work, based on a novel parameter-free discontinuity-detection criterion, a new shock-capturing framework is proposed by combining the standard TENO (targeted essentially non-oscillatory) scheme for smooth regions with the non-polynomial based THINC (tangent of hyperbola for INterface capturing) reconstruction for non-smooth discontinuities. The resulting hybrid scheme retains the low-dissipation property of TENO scheme for smooth flow scales and the discontinuity-resolving capability of THINC reconstruction for shock and contact waves. A set of benchmark simulations involving a wide range of length scales demonstrates that the new TENO-THINC scheme performs significantly better than the standard TENO scheme without the necessity of parameter tuning case by case, and thus is promising for more complex compressible flow predictions where the excessive numerical dissipation of existing schemes prevents the targeted flow structures from being properly resolved. Moreover, the present results serve as the state-of-the-art references for future numerical method development.

An efficient low-dissipation high-order TENO scheme for MHD flows

In this paper, an efficient low-dissipation high-order TENO scheme is proposed for ideal MHD flows. For high computational efficiency, a troubled-cell indicator based on the ENO-like stencil selection strategy in TENO schemes is introduced to isolate the discontinuities from smooth regions. While the high-order linear scheme is adopted for the smooth regions, a low-dissipation TENO scheme is applied for capturing discontinuities detected by the troubled-cell indicator. The case-independent parameters are given based on spectral analysis. Both the governing equations of the ideal MHD and the Hamilton-Jacobi type constrained transport equation for divergence-free condition can be solved by the newly proposed scheme. Since most computational regions are resolved by the linear scheme without expensive characteristic decomposition, flux splitting and nonlinear weight calculation, the proposed scheme is highly efficient. A set of benchmark cases has been simulated to demonstrate the performance of the proposed scheme. Numerical results reveal that remarkable speedup is achieved by the present scheme while the oscillation-free property and the high-order accuracy are preserved.